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This paper presents robust estimators for binary and multinomial circular logistic regression, where a circular predictor is related to the response. An extensive Monte Carlo Simulation Study clearly shows the robustness of proposed methods. Finally, three numerical examples of Botany, Crime and Meteorology illustrate the application of these methods to Life and Social Sciences. Although in the Botany data the proposed method showed little improvement, in the Crime and Meteorological data an increment up to 5% and 4% of accuracy, respectively, is achieved. [ABSTRACT FROM AUTHOR]

Asymmetric probability distributions have been widely studied by various authors in recent decades. Special interest has been had families of flexible distributions with the capability to have into account degree of skewness and kurtosis greater than the classical distributions widely known in statistical theory. While, most of the new distributions _t unimodal data, and a few fit bimodal data, in the bimodal proposals, singularity problems have been found in the information matrices. Therefore, in this paper, extensions of the alpha-power family of distributions are developed, which have non-singular information matrix. The new proposals are based on the bimodal-normal and bimodal elliptical skew-normal distributions. These new extensions allow modeling asymmetric bimodal data, which are commonly found in several areas of scientific interest. The properties of these new distributions of probability are also studied in detail, and the statistical inference process is carried out to estimate the parameters of the proposed models. The stochastic convergence for the maximum likelihood estimator (MLE) vector can be found due to the non-singularity of the expected information matrix in the corresponding support. We also introduced extensions of the asymmetric bimodal normal and bimodal elliptical skew-normal models for the situations in which the data present censorship. A small simulation study to evaluate the properties of the MLE is also presented and, finally, two applications to real data set are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

Assumption of normality in statistical analysis had been a common practice in many literature, but in the event where small sample is obtainable, then normality assumption will lead to erroneous conclusion in the statistical analysis. Taking a large sample had been a serious concern in practice due to various factors. In this paper, we further derived some inferential properties for log student's t-distribution (simply log-t distribution) which makes it more suitable as substitute to log-normal when carrying out analysis on right-skewed small sample data. Mathematical and Statistical properties such as the moments, cumulative distribution function, survival function, hazard function and log-concavity are derived. We further extend the results to case of multivariate log-t distribution; we obtained the marginal and conditional distributions. The parameters estimation was done via maximum likelihood estimation method, consequently its best critical region and information matrix were derived in order to obtain the asymptotic confidence interval. The applications of log-t distribution and goodness-of-fit test was carried out on two dataset from literature to show when the model is most appropriate. [ABSTRACT FROM AUTHOR]

In this paper we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model. The maximum likelihood estimate of the reliability parameter and its asymptotic con- fidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented. Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes estimate of the reliability. To evaluate the performances of different procedures, simulation studies are conducted and an example of real data sets is provided. [ABSTRACT FROM AUTHOR]

The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the suficient and minimal suficient statistics, maximum likelihood estimation and the Fisher information matrix are studied. [ABSTRACT FROM AUTHOR]

The alpha-skew normal (ASN) distribution has been proposed recently in the literature by using standard normal distribution and a skewing ap- proach. Although ASN distribution is able to model both skew and bimodal data, it is shortcoming when data has thinner or thicker tails than normal. Therefore, we propose an alpha-skew generalized t (ASGT) by using the gen- eralized t (GT) distribution and a new skewing procedure. From this point of view, ASGT can be seen as an alternative skew version of GT distribution. However, ASGT differs from the previous skew versions of GT distribution since it is able to model bimodal data sest as well as it nests most commonly used density functions. In this paper, moments and maximum likelihood estimation of the parameters of ASGT distribution are given. Skewness and kurtosis measures are derived based on the first four noncentral moments. The cumulative distribution function (cdf) of ASGT distribution is also ob- tained. In the application part of the study, two real life problems taken from the literature are modeled by using ASGT distribution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as Beta-exponential and generalized Gompertz distributions as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function, Shannon entropy, and the quantile measure are provided. We discuss maximum likelihood estimation of the BG parameters from one observed sample and derive the observed Fisher's information matrix. A simulation study is performed in order to investigate the properties of the proposed estimator. At the end, in order to show the BG distribution flexibility, an application using a real data set is presented. [ABSTRACT FROM AUTHOR]